Four regimes of self-assembly determined by the parameter χ = (f·l0)/(Δμ0). The curves represent the total protein flux, J(arbitrary units), to the aggregate as a function of the aggregate length, L(arbitrary units). (a) Atχ < 1, and χ < χ*, the flux is negative, meaning that the aggregate undergoes disintegration. (b) At χ > 1, and χ > χ*, the flux is positive, meaning that the aggregate undergoes unlimited growth. (c) At χ < 1 but χ > χ*, the flux is negative until the aggregate reaches a certain length where the flux changes sign and starts increasing with the aggregate length. This regime corresponds to unlimited growth after overcome of a critical length. (d) At χ > 1 and χ <χ*, the flux remains positive until the aggregate reaches a critical length. For length larger than the critical values, the flux is negative. This state is the steady-state regime, where the critical length corresponds to the stable steady-state length of the aggregate.